Question

you have $5.00 in quarters and dimes. you have a total of 41 coins. how many of the coins are quarters?

Answer 1

So, from this information you can set up two equations:
0.1x + 0.25y = 5 dollars and
x + y = 41 coins
where x = how many dimes and y = how many quarters

Solve for either x or y in the second equation, so x = 41 - y and then plug this in for x in the first equation to get:
0.1(41 - y) + 0.25y = 5
4.1 - 0.1y + 0.25y = 5
4.1 + 0.15y = 5
0.15y = 0.9
y = 6
We solved for y and now we know there are 6 quarters, so you can plug this into the second equation to solve for x. We fine that we have 35 dimes. You can always your work by plugging what you get for x and y back into the equations.